Height of Mt. Everest (History and the Science behind)

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How do they measure the height of Mt. Everest for the first time? OR How do we get the number 8848 m? Well the straightforward answer could be by using the GPS technology. But GPS technology evolved only by the end of millennium. Whereas, we knew about the height of Everest even before that. So,let’s try to investigate the details of: How the height of Mt. Everest measured for the first time? Making the question simpler: How do we measure the height of any mountain?

At the heart of measuring, the height of any mountain relies on the basic concept of trigonometry. The way it works is in any right-angled triangle, by knowing the value of an angle and the distance of the specific side: you can work out the height of a triangle which is your height of mountain. Therefore, the work starts firstly by assuming a big triangle in your working field. For this, you set three points: One at the tip of mountain, second at the base of mountain and the final point is your position at the ground.  Here, you measure the angle of the tip of mountain and then the distance between you and the mountain. But wait!! What if you cannot measure this big distance. In that case walk towards the mountain and measure the second angle from the new position. In this way you have two angles measured from two positions in ground.On top of that you also know the distance between you initial and final position in the ground. Now you can put those values back into your trigonometric mantra and play with the equation a bit here and there: which will give you back the height of mountain.But wait!! this is just the height of mountain from your position. For complete picture, you must add the extra height of your location from sea level. The final value which you obtain is the height of the mountain with respect to sea level. Finding the height of mountain, it might seem easy;Well in practice, it is not. Because every information you collect at the ground is associated with an error and the game is about the knowing and applying the correction factors which will reduce your errors.

Let’s try to see, some of these errors:

Refraction of light: light passing from one medium to another medium is refracted or in another word it bends. This means the light travelling from tip of mountain to your eyes is bent by atmosphere – as a result of which you see the tip of mountain slightly at wrong position. Or in observational term the measured angle of inclination is blurred. Kind of a similar effect which makes starts to twinkle even though stars are just glowing mass of objects.Another very prominent effect of atmospheric refraction causes the Sun rise couple of minutes earlier and Sun set couple of minutes later thus allowing us to gain some minutes every day than we disserve. Such error introduced by refraction must be minimized while measuring the angle. Which can be done with an appropriate knowledge of temperature and pressure of atmospheric layers.  There are of-course rigorous theoretical formula and several kinds of assumptions in order to minimize the error. One of the ways to minimize the error has been to do the act of measurement during mid-day when variation in the temperature gradient are least.

Curvature of Earth: Yes, Earth is not flat; it is approximately spherical in shape,so an error is introduced in any significantly large measured horizontal distance. A correction factor considering the curvature and radius of Earth must be added for accurate distance measurements.

The word sea water level might remind you a well-known property of water i.e. it maintains its level when kept in any irregular shape vessel. Meaning the seawater kept or confined in irregular shape of Earth should also maintain same level everywhere.However, you are missing the important point here i.e the water in planet Earth is hold by its gravity.What if I say, The gravity is not same everywhere around the earth due to its irregular interior density. That means, the water accumulates and increases the level in stronger gravity area then in the weaker one. In addition to that, the mountain itself is a huge chunk of mass causing higher gravitational pull to the water area around. Also let’s not forget the rotation of the Earth causes the water to accumulate more in the equatorial region then in the poles.With the help of mathematic and logical reasoning this conundrum has been solved to the greater extent nowadays.

Beside above mention errors or required correction factors, several other uncertainties also have to be taken into consideration:  the variation of snow on top of Everest from one season to another and error like plumb line deflection, which arises due to labelling of the observational ground.

Getting back to our history: During the period in between 1840-50: British surveyor Andrew Waugh and his team measured the height of the tallest mountain: Mt. Everest (local name Sagarmatha). Since closure, approach to Nepal was denied in that period. They placed six stations very far from the mountain (length ranging from 174 to 192 km) at the plains of Bengal in India. An observational tower was established at each location where his team members performed rigorous measurements for years. Those locations were at the height of 70 meter from the sea level. There are criticism and several arguments on the values of refractive index used by him in order to minimize the error introduced by refraction. But I would simply like to admire his drive in getting those observation and computing the data. The mean height computed from all these observations was 8839.80 meter and that was the height of mountain Everest known for the first time.

In coming years, several other observations were performed from hills of Darjeeling and even from closure distance like Namche Bazar. Ever since there has been many debates/extra measurements conducted in order to minimize the errors and get the precise value of the height. Nevertheless, we are still using the value, which is very close to the first observation with an extra modification by adding 8.2 meter: thus, making a total of 8848 meter.

Have you ever consider that this number 8848 will not be the fixed height of Mt. Everest forever?Yes! the Himalayan mountains are not stable: they are rising and up every year. More on that some other time.

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